IEEE Transactions on Information Theory最新文献_第2页

IEEE Transactions on Information Theory Publication Information IEEE信息论学报，出版信息

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-24 DOI: 10.1109/TIT.2025.3560573

引用次数: 0

Sharp Convergence Rates for Matching Pursuit 匹配追踪的快速收敛速度

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-24 DOI: 10.1109/TIT.2025.3564227

Jason M. Klusowski;Jonathan W. Siegel

{"title":"Sharp Convergence Rates for Matching Pursuit","authors":"Jason M. Klusowski;Jonathan W. Siegel","doi":"10.1109/TIT.2025.3564227","DOIUrl":"https://doi.org/10.1109/TIT.2025.3564227","url":null,"abstract":"We study the fundamental limits of matching pursuit, or the pure greedy algorithm, for approximating a target function <italic>f by a linear combination <inline-formula> <tex-math>$f_{n}$ </tex-math></inline-formula> of <italic>n elements from a dictionary. When the target function is contained in the variation space corresponding to the dictionary, many impressive works over the past few decades have obtained upper and lower bounds on the error <inline-formula> <tex-math>$|f-f_{n}|$ </tex-math></inline-formula> of matching pursuit, but they do not match. The main contribution of this paper is to close this gap and obtain a sharp characterization of the decay rate, <inline-formula> <tex-math>$n^{-alpha }$ </tex-math></inline-formula>, of matching pursuit. Specifically, we construct a worst-case dictionary which shows that the best-known upper bound cannot be substantially improved. It turns out that, unlike other greedy algorithm variants which converge at the optimal rate of <inline-formula> <tex-math>$ n^{-1/2}$ </tex-math></inline-formula>, the convergence rate of <inline-formula> <tex-math>$n^{-alpha }$ </tex-math></inline-formula> is suboptimal. Here, <inline-formula> <tex-math>$alpha approx 0.182$ </tex-math></inline-formula> is determined by the solution to a certain non-linear equation.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5556-5569"},"PeriodicalIF":2.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

IEEE Transactions on Information Theory Information for Authors IEEE信息理论汇刊：作者信息

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-24 DOI: 10.1109/TIT.2025.3560575

引用次数: 0

On Low-Power Error-Correcting Cooling Codes With Large Distances 大距离低功耗纠错冷却码研究

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-24 DOI: 10.1109/TIT.2025.3563973

Yuhao Zhao;Xiande Zhang

{"title":"On Low-Power Error-Correcting Cooling Codes With Large Distances","authors":"Yuhao Zhao;Xiande Zhang","doi":"10.1109/TIT.2025.3563973","DOIUrl":"https://doi.org/10.1109/TIT.2025.3563973","url":null,"abstract":"A low-power error-correcting cooling (LPECC) code was introduced as a coding scheme for communication over a bus by Chee et al. to control the peak temperature, the average power consumption of on-chip buses, and error-correction for the transmitted information, simultaneously. Specifically, an <inline-formula> <tex-math>$(n, t, w, e)$ </tex-math></inline-formula>-LPECC code is a coding scheme over <italic>n wires that avoids state transitions on the <italic>t hottest wires and allows at most <italic>w state transitions in each transmission, and can correct up to <italic>etransmission errors. In this paper, we study the maximum possible size of an <inline-formula> <tex-math>$(n, t, w, e)$ </tex-math></inline-formula>-LPECC code, denoted by <inline-formula> <tex-math>$C(n,t,w,e)$ </tex-math></inline-formula>. When <inline-formula> <tex-math>$w=e+2$ </tex-math></inline-formula> is large, we establish a general upper bound <inline-formula> <tex-math>$C(n,t,w,w-2)leq lfloor binom {n+1}{2}/binom {w+t}{2}rfloor $ </tex-math></inline-formula>; when <inline-formula> <tex-math>$w=e+2=3$ </tex-math></inline-formula>, we prove <inline-formula> <tex-math>$C(n,t,3,1) leq lfloor frac {n(n+1)}{6(t+1)}rfloor $ </tex-math></inline-formula>. Both bounds are tight for large <italic>n satisfying some divisibility conditions. Previously, tight bounds were known only for <inline-formula> <tex-math>$w=e+2=3,4$ </tex-math></inline-formula> and <inline-formula> <tex-math>$tleq 2$ </tex-math></inline-formula>. In general, when <inline-formula> <tex-math>$w=e+d$ </tex-math></inline-formula> is large for a constant <italic>d, we determine the asymptotic value of <inline-formula> <tex-math>$C(n,t,w,w-d)sim binom {n}{d}/binom {w+t}{d}$ </tex-math></inline-formula> as <italic>n goes to infinity, which can be extended to <italic>q-ary codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5215-5225"},"PeriodicalIF":2.2,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient Federated Low Rank Matrix Completion 高效联邦低秩矩阵补全

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-23 DOI: 10.1109/TIT.2025.3563450

Ahmed Ali Abbasi;Namrata Vaswani

{"title":"Efficient Federated Low Rank Matrix Completion","authors":"Ahmed Ali Abbasi;Namrata Vaswani","doi":"10.1109/TIT.2025.3563450","DOIUrl":"https://doi.org/10.1109/TIT.2025.3563450","url":null,"abstract":"In this work, we develop and analyze a novel Gradient Descent (GD) based solution, called Alternating GD and Minimization (AltGDmin), for efficiently solving the low rank matrix completion (LRMC) in a federated setting. Here “efficient” refers to communication-, computation- and sample- efficiency. LRMC involves recovering an <inline-formula> <tex-math>$n times q$ </tex-math></inline-formula> rank-<italic>r matrix <inline-formula> <tex-math>${boldsymbol {X}}^{star } $ </tex-math></inline-formula> from a subset of its entries when <inline-formula> <tex-math>$r ll min (n,q)$ </tex-math></inline-formula>. Our theoretical bounds on the sample complexity and iteration complexity of AltGDmin imply that it is the most communication-efficient solution while also been one of the most computation- and sample-efficient ones. We also extend our guarantee to the noisy LRMC setting. In addition, we show how our lemmas can be used to provide an improved sample complexity guarantee for the Alternating Minimization (AltMin) algorithm for LRMC. AltMin is one of the fastest centralized solutions for LRMC; with AltGDmin having comparable time cost even for the centralized setting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5493-5511"},"PeriodicalIF":2.2,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Research on the Construction of Maximum Distance Separable Codes via Arbitrary Twisted Generalized Reed-Solomon Codes 利用任意扭曲广义Reed-Solomon码构造最大距离可分码的研究

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-23 DOI: 10.1109/TIT.2025.3563664

Chun'e Zhao;Wenping Ma;Tongjiang Yan;Yuhua Sun

引用次数: 0

Compute-Forward Multiple Access for Gaussian Fast Fading Channels 高斯快速衰落信道的计算前向多址

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-21 DOI: 10.1109/TIT.2025.3560447

Lanwei Zhang;Jamie Evans;Jingge Zhu

{"title":"Compute-Forward Multiple Access for Gaussian Fast Fading Channels","authors":"Lanwei Zhang;Jamie Evans;Jingge Zhu","doi":"10.1109/TIT.2025.3560447","DOIUrl":"https://doi.org/10.1109/TIT.2025.3560447","url":null,"abstract":"Compute-forward multiple access (CFMA) is a transmission strategy which allows the receiver in a multiple access channel (MAC) to first decode linear combinations of the transmitted signals and then solve for individual messages. Compared to existing MAC strategies such as joint decoding or successive interference cancellation (SIC), CFMA was shown to achieve the MAC capacity region for fixed channels under certain signal-to-noise (SNR) conditions without time-sharing using only single-user decoders. This paper studies the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). We investigate appropriate lattice decoding schemes to decode linear combinations with any integer coefficients in the fading MAC and derive the achievable rate pairs. We give a sufficient and necessary condition under which the proposed scheme can achieve the ergodic sum capacity. Furthermore, we investigate the impact of channel statistics on the capacity achievability of the CFMA scheme. In general, the sum capacity is achievable if the channel variance is small compared to the mean value of the channel strengths. Various numerical results are presented to illustrate the theoretical findings.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4112-4124"},"PeriodicalIF":2.2,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact and Local Compression of Quantum Bipartite States 量子二部态的精确和局部压缩

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-21 DOI: 10.1109/TIT.2025.3562884

Kohtaro Kato

引用次数: 0

Optimal Codes Correcting a Substring Edit 修正子字符串编辑的最优代码

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-21 DOI: 10.1109/TIT.2025.3562730

Yuting Li;Yuanyuan Tang;Hao Lou;Ryan Gabrys;Farzad Hassanzadeh Farnoud

{"title":"Optimal Codes Correcting a Substring Edit","authors":"Yuting Li;Yuanyuan Tang;Hao Lou;Ryan Gabrys;Farzad Hassanzadeh Farnoud","doi":"10.1109/TIT.2025.3562730","DOIUrl":"https://doi.org/10.1109/TIT.2025.3562730","url":null,"abstract":"The substring edit error replaces a substring <inline-formula> <tex-math>$boldsymbol {u}$ </tex-math></inline-formula> of <inline-formula> <tex-math>$boldsymbol {x}$ </tex-math></inline-formula> with another string <inline-formula> <tex-math>$boldsymbol {v}$ </tex-math></inline-formula>, where the lengths of <inline-formula> <tex-math>$boldsymbol {u}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$boldsymbol {v}$ </tex-math></inline-formula> are bounded by a given constant <italic>k. It encompasses localized insertions, deletions, and substitutions within a window. Codes correcting one substring edit have redundancy at least <inline-formula> <tex-math>$log n+k$ </tex-math></inline-formula>. In this paper, we construct codes correcting one substring edit with redundancy <inline-formula> <tex-math>$log n+O_{k}(log log n)$ </tex-math></inline-formula>, which is almost optimal. We also study the average-case document-exchange problem under one substring edit and construct a hash with an expected length of approximately <inline-formula> <tex-math>$2log n+O_{k}(log log n)$ </tex-math></inline-formula> for any iid distribution for the documents.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5178-5191"},"PeriodicalIF":2.2,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Encoding of Algebraic Geometry Codes With Quasi-Linear Complexity O(NlogN) 拟线性复杂度O（NlogN）代数几何码的编码

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-04-18 DOI: 10.1109/TIT.2025.3562424

Songsong Li;Shu Liu;Liming Ma;Yunqi Wan;Chaoping Xing

{"title":"Encoding of Algebraic Geometry Codes With Quasi-Linear Complexity O(NlogN)","authors":"Songsong Li;Shu Liu;Liming Ma;Yunqi Wan;Chaoping Xing","doi":"10.1109/TIT.2025.3562424","DOIUrl":"https://doi.org/10.1109/TIT.2025.3562424","url":null,"abstract":"Fast encoding and decoding of codes have always been an important topic in coding theory as well as complexity theory. Although encoding is easier than decoding in general, designing an encoding algorithm of codes of length <italic>N with quasi-linear complexity <inline-formula> <tex-math>$O(Nlog N)$ </tex-math></inline-formula> is not an easy task. Despite of the fact that algebraic geometry codes (AG codes) were discovered in the early 1980s, encoding algorithms of algebraic geometry codes with quasi-linear complexity <inline-formula> <tex-math>$O(Nlog N)$ </tex-math></inline-formula> have not been found except for the simplest algebraic geometry codes-Reed-Solomon codes. The best-known encoding algorithm of algebraic geometry codes based on a class of plane curves has quasi-linear complexity at least <inline-formula> <tex-math>$O(Nlog ^{2} N)$ </tex-math></inline-formula> (Beelen et al. IEEE Trans. Inf. Theory 2021). In this paper, we design an encoding algorithm for algebraic geometry codes with quasi-linear complexity <inline-formula> <tex-math>$O(Nlog N)$ </tex-math></inline-formula>. Moreover, for these fast encodable AG codes, the inverse of encoding, that is, interpolating the message function from the corresponding codeword, can be computed with the same complexity <inline-formula> <tex-math>$O(Nlog N)$ </tex-math></inline-formula>. Our algorithms are applicable to a large class of algebraic geometry codes based on both plane and non-plane curves, including Kummer extensions, Artin-Schreier extensions, and Hermitian field towers.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5013-5026"},"PeriodicalIF":2.2,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0